A claim or statement that is alleged hasn't been proven true — if you're an alleged murderer, you've been accused but not convicted.
When a fact is alleged there is doubt about its accuracy. If you watch crime dramas, a lawyer will often say, "It is alleged my client committed murder, but he couldn't have done it!" This word is often used in connection with court cases, because the accused is innocent until proven guilty. Journalists often use alleged in news stories when someone’s guilt is suspected but not confirmed. Sometimes alleged means doubtful or dubious, as in "Who is this alleged expert?"